Related papers: Noetherian Operators in Macaulay2
A finitely generated module C over a commutative noetherian ring R is semidualizing if Hom_R(C,C) \cong R and Ext^i_R(C,C) = 0 for all i \geq 1. For certain local Cohen-Macaulay rings (R,m), we verify the equality of Hilbert-Samuel…
We present an algorithm to compute a primary decomposition of an ideal in a polynomial ring over the integers. For this purpose we use algorithms for primary decomposition in polynomial rings over the rationals resp. over finite fields, and…
The article targets binomial ideals in quantum tori and quantum affine spaces. First, noncommutative analogs of known results for commutative (Laurent) polynomial rings are obtained, including the following: Under the assumption of an…
We propose a numerical linear algebra based method to find the multiplication operators of the quotient ring $\mathbb{C}[x]/I$ associated to a zero-dimensional ideal $I$ generated by $n$ $\mathbb{C}$-polynomials in $n$ variables. We assume…
Ore operators form a common algebraic abstraction of linear ordinary differential and recurrence equations. Given an Ore operator $L$ with polynomial coefficients in $x$, it generates a left ideal $I$ in the Ore algebra over the field…
This paper has two aims. The first is to study ideals of minors of matrices whose entries are among the variables of a polynomial ring. Specifically, we describe matrices whose ideals of minors of a given size are prime. The main result in…
First, we study the subskewfield of rational pseudodifferential operators over a differential field K generated in the skewfield of pseudodifferential operators over K by the subalgebra of all differential operators. Second, we show that…
The set of the first Hilbert coefficients of parameter ideals relative to a module--its Chern coefficients--over a local Noetherian ring codes for considerable information about its structure--noteworthy properties such as that of…
If $\fg$ is a semisimple Lie algebra, we describe the prime factors of $\mcU(\fg)$ that have enough finite dimensional modules. The proof depends on some combinatorial facts about the Weyl group which may be of independent interest. We also…
The aim of this paper is to classify the bispectral operators of any rank with regular singular points (the infinite point is the most important one). We characterise them in several ways. Probably the most important result is that they are…
This paper investigates the Poisson geometry associated to a cluster algebra over the complex numbers, and its relationship to compatible torus actions. We show, under some assumptions, that each Noetherian cluster algebra has only finitely…
This study is an attempt at generalizing the class of partially hypoelliptic differential operators to a class of pseudodifferential operators, Symbol ideals are formed on the set of lineality and we discuss suitable topologies that allow…
In this paper, we define a new concept of Noetherian commutative rings which stands between Gorenstein and Cohen-Macaulay properties. We show that this new property keep hold under common operations of commutative rings such as…
We introduce mixed Morrey spaces and show some basic properties. These properties extend the classical ones. We investigate the boundedness in these spaces of the iterated maximal operator, the fractional integtral operator and singular…
After sketching the basic theory of injective ideals of homogeneous polynomials, we characterize injective polynomial ideals by means of a domination property and applications of this characterization to some classical operator ideals and…
In this paper we study the set of prime ideals in vector lattices and how the properties of the prime ideals structure the vector lattice in question. The different properties that will be considered are firstly, that all or none of the…
Representations of polynomial covariance commutation relations by pairs of linear integral and differential operators are constructed in the space of infinitely continuously differentiable functions. Representations of polynomial covariance…
We use linear algebraic methods to obtain general results about linear operators on a space of polynomials that we apply to the operators associated with a polynomial sequence by the monomiality property. We show that all such operators are…
We define marked sets and bases over a quasi-stable ideal $\mathfrak j$ in a polynomial ring on a Noetherian $K$-algebra, with $K$ a field of any characteristic. The involved polynomials may be non-homogeneous, but their degree is bounded…
We characterize symbolic powers of prime ideals in polynomial rings over any field in terms of $\mathbb{Z}$-linear differential operators, and of prime ideals in polynomial rings over complete discrete valuation rings with a $p$-derivation…